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Chapter 3: Q. 29 (page 314)
L’Hˆopital’s Rule limit calculations: Calculate each of the
limits that follow. Some of these limits are easier to calculate
by using L’Hopital’s rule, and some are not.
Limit is one and it is easy to find using L'Hospital rule.
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Find the critical points of the function
Sketch the graph of a function f with the following properties:
f is continuous and defined on R;
f(0) = 5;
f(−2) = −3 and f '(−2) = 0;
f '(1) does not exist;
f' is positive only on (−2, 1).
Use a sign chart for to determine the intervals on which each function is increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.
Calculate each of the limits in Exercises 15–20 (a) using
L’Hopital’s rule and (b) without using L’H ˆ opital’s rule.
Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility.
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